Hi Bob,
The speedometer in the Healey is not an easy rebuild as the accuracy is set by a light resisting spring which is installed behind a concave disk. As I remember, the cable, attached to 2 magnets riding within the concave disk, spins fast and creates a magnetic force which pull the disk in the direction of the spin. The faster the cable/magnets spin, the more the disk is pulled/turns and overcomes the resistance of a counter force applied by a spring. Since the needle is attached to the disk side of the coupling (cable-magnets, disk-needle) as the disk moves, the needle moves. Gauge accuracy is achieved by establishing the proper balance of generated magnet spin to the net of spring disk movement and spring resistance. As I see it, without proper equipment, it will be almost impossible to set the complex of forces to achieve an proper needle reading.
If I had your problem of jammed speedometer, I would take a shot as it would be almost certain to need a professional fix. After removing the cable from the back of the speedometer, I would disconnect the transmission end and spin the cable within its sheath to be sure your jam is not in the cable. If the cable seem free and spins without difficulty, I would then remove the speedometer from the dash and remove the front glass and rear 2 retaining screws. This will allow the removal of the full speedometer form its case and expose major components.
Keep in mind that I am not an expert on this subject but I have experienced some problems that cleaning has close to resolved. One issue was when too much lubricant was inserted into the speedometer cable sheath and, passing the upper seal, collected and hardened within the concave disk. This lubricant caused the magnet to jam in the disk and twist the disk off its pivots. After cleaning, although I was able to reset the disk onto its spindle, the retaining spring was forced and needed to be replaced and reset by a professional.
Bob, although I do not hold high hope that you will be able to achieve a speedometer fix, cable, angle-drive, and lubrication may be outside issues that can be corrected. Still and all, since a professional fix is likely to be needed to achieve a gauge fix, I would carefully expose the internals of the gauge to better understand its operation. Although I would have no hesitation disassembling any other gauge, the speedometer is the one I hesitate dealing with.
Sorry for the less-than-encouraging presentation,
Ray(64BJ8P1)